Question: Solve for $x$ and $y$ using elimination. ${-3x+2y = 6}$ ${3x-3y = -15}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. $-y = -9$ $\dfrac{-y}{{-1}} = \dfrac{-9}{{-1}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {-3x+2y = 6}\thinspace$ to find $x$ ${-3x + 2}{(9)}{= 6}$ $-3x+18 = 6$ $-3x+18{-18} = 6{-18}$ $-3x = -12$ $\dfrac{-3x}{{-3}} = \dfrac{-12}{{-3}}$ ${x = 4}$ You can also plug ${y = 9}$ into $\thinspace {3x-3y = -15}\thinspace$ and get the same answer for $x$ : ${3x - 3}{(9)}{= -15}$ ${x = 4}$